The most important consequence of magnetic fields is that they increase the phase space for neutral mesons;
at large \(B\) , the phase space enhancement of a factor \(\sim (1-\eta )^{-1} \sim |B|^2/\Lambda _{\rm QCD}^4\)  takes place.
At low temperature where the lightest neutral mesons dominate,
the entropy density is significantly larger at finite \(B\)  than the \(B=0\)  case.
This tendency is very different from the PDG based HRG at finite \(B\) , where neutral states are treated as elementary and do not depend on \(B\) ;
the resulting entropy density is much smaller than ours and lattice results for \(eB\gtrsim 0.1\,{\rm GeV}^2\) , see Fig.10 in Ref.[1]}.
